The magnetization of neutron star matter in magnetic fields is studied by employing the FSUGold interaction. It is found that the magnetic susceptibilities of the charged particles (proton, electron and muon) can be larger than that of neutron. The effects of the anomalous magnetic moments (AMM) of each component on the magnetic susceptibility are examined in detail. It is found that the proton and electron AMM affect their respective magnetic susceptibility evidently in strong magnetic fields. In addition, they are the protons instead of the electrons that contribute most significantly to the magnetization of the neutron star matter in a relative weak magnetic field, and the induced magnetic field due to the magnetization can be appear to be very large. Finally, the effect of the density-dependent symmetry energy on the magnetization is discussed.